These are some project ideas that we (Ashley, Nora, and Margaret) are excited about!

1. Flower Tilings

This project seems interesting because our group was talking about combining flowers with mathematics. I’ve (Ashley) been really into flower pressing and drying for the past couple of years and have seen that flowers can be related to math through the Fibonacci sequence (through the number of petals or even seed patterns landing on a Fibonacci number). So we thought that tilings could be a way to use flowers through art and represent mathematics.

We’re considering using Einstein tilings (left) or Penrose tilings (right) to do this.

Einstein tiles are a single design of tile that fit together perfectly, but never form a pattern that repeats. This is a 13-sided shape. Penrose tilings use two different tiles (both 4 sided) to create an aperiodic tiling.

We were hoping to cut out these tilings with flower petals and leaves, and create flower tilings out of them. The making process would consist of collecting the flowers either from outside or buying them, then pressing the flowers and leaves flat to make them easier to work with. Next, we would cut out the flower petals and leaves through creating a stencil with the laser cutter of the Einstein or Penrose tiles on wood/paper, and use the stencil to cut out the shape from the flowers using an Exactoknife.

A link that could be useful to us is: https://www.scientificamerican.com/article/newfound-mathematical-einstein-shape-creates-a-never-repeating-pattern/

2. Visualizing the fourier transform?? (GONE WRONG??!) (NOT CLICKBAIT‼️‼️) 🤯🤯

It would be super awesome to visualize sound waves and the fourier transform in some fun way! Mathus mentioned a Python library that could generate spectrograms in class:

scipy.signal.spectrogram — SciPy v1.12.0 Manual (maybe this? 😱)

But we also see some people building arduinos with little lights that respond to noise!:

https://1littleendian.medium.com/the-late-night-tinkering-projects-10-fun-with-fourier-a72b358229b3

This 3blue1brown video is so fire 🤩🤩:

Ideally we’d love to build something that visually represents the fourier transform and then maybe also has some way of generating cool visuals? This project could go a lot of directions and could utilize a ton of new tools—- I’d (Nora) like to get more comfortable coding and working in python but arduinos would be cool as well. The fourier transform is also super important for spectroscopy and I’d love to understand some of the instruments I use in labs better!!! There are tons of people at mudd/alums who have been doing stuff similar to this so even though we personally might not have the most experience in this area I think we could get some guidance! This would be a pretty ambitious project because idk if we have a ton of background knowledge but that also means we could learn a lot from it! 🤠🤠 😁😁

3. Tensegrity structure

I (Margaret) don’t have much experience with hands-on mechanical design, but my group is most interested in producing tension integrity art.

What it is:

• Tensegrity is in principle the manipulation of pulling tensions of shapes varying in size/shape/material that are connected with any type of sturdy string such as ropes, wire, or chains 
• https://www.researchgate.net/profile/Robert-Skelton-4/publication/3934570_An_introduction_to_the_mechanics_of_tensegrity_structures/links/00b7d521cc69481ac7000000/An-introduction-to-the-mechanics-of-tensegrity-structures.pdf

Math concepts:

• Distribution of mass
• Tension and compression
• Equilibrium
• Axial loads
• Geometry/mechanics

Making process:

• Machine shop: cut wooden shapes with saws, sand too
• I used to work in the wood shop a lot in my high school! So I know how to do some stuff (-Nora)